SOLUTION: Alice stopped by a coffee shop two days in a row at a conference to buy drinks and
pastries. On the first day, she bought a cup of coffee and two muffins for which she
paid |6.87
Question 1181953: Alice stopped by a coffee shop two days in a row at a conference to buy drinks and
pastries. On the first day, she bought a cup of coffee and two muffins for which she
paid |6.87. The next day she bought two cups of coffee and three muffins (for herself
and a friend). Her bill was |11.25. Use the method of elimination to determine the
price of a cup of coffee, and the price of a muffin. Clearly explain your set-up for the
problem
2 x + 3.00 y = 11.25 .............2
Eliminate y
multiply (1)by -3
Multiply (2) by 2
-3 x -6 y = -20.61
4 x 6 y = 22.50
Add the two equations
1.00 x = 1.89
/ 1.00
x = 1.89
plug value of x in (1)
1.00 x + 2.00 y = 6.87
1.89 + 2.00 y = 6.87
2.00 y = 4.98
y = 2.49
Ans
$ 1.89 Price of one coffee
$ 2.49 Price of one muffin
Here is a different path to the solution. Not the most efficient path; but if you are good with mental arithmetic this method can allow you to solve the problem mentally.
Given:
2 cups of coffee and 3 muffins cost $11.25 : 2x+3y=11.25 [1]
1 cup of coffee and 2 muffins cost $6.87 : x+2y=6.87 [2]
Comparing those two purchases tells us
1 cup of coffee and 1 muffin cost $11.25-$6.87 = $4.38 : x+y=4.38 [3]
Now use elimination using [2] and [3]: multiply [3] by -1 and add to [2] to give
y=6.87-4.38=2.49 [4]
Then use [3] and [4] to find x=4.38-2.49=1.89
ANSWERS: coffee x=$1.89; muffin y=$2.49
Mentally, the solution goes something like this:
2 coffees and 3 muffins cost $11.25
1 coffee and 2 muffins cost $6.87
So 1 less coffee and 1 less muffin costs $11.25=$6.87=$4.38 less
Taking away 1 coffee and 1 muffin again leaves one muffin, at a cost of $6.87-$4.38=$2.49
Then the cost of the coffee is $4.38-$2.49=$1.89
